


Gödel, Escher, Bach: An Equiod Rolling Hay

by Slant



Category: Gödel Escher Bach: An Eternal Golden Braid, My Little Pony: Friendship is Magic
Genre: Recursion, Zeno's arrow paradox, meta-cognition
Language: English
Status: Completed
Published: 2013-10-08
Updated: 2013-10-08
Packaged: 2017-12-28 20:57:07
Rating: Not Rated
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 531
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/996624
Author URL: https://archiveofourown.org/users/Slant/pseuds/Slant
Summary: <blockquote class="userstuff">
              <p>I'm pretty sure no one will ever look for FIM, GEB crossover fan fiction, but if you did and you found this, um, well done, the internet provides :)</p>
            </blockquote>





	Gödel, Escher, Bach: An Equiod Rolling Hay

It was a nice day in Ponyville. Mr Tortoise, who was there to visit his friend Tank and to engage in some applied meta-cognition with Rainbow Dash, fleetest of wing of all mortals, glared at the opening sentence for being information-poor: it is axiomatic that days in Ponyville are nice, so saying that something is both nice and a day in Ponyville offended his artistic sensibilities.

...

"One of the most fascinating aspects of true intelligence is that, while it can ploddingly, mechanically, tie itself to some rule and apply it, rapidly and without conscious effort, it can also break out of those same bonds in ways which are not included in the rule. There are few computer-playing chess programs that get angry, punch out their opponent and rummage through their pockets for coppers, but the meanest of Pony or Tortoise players, even if not familiar with the gambit, will be well capable of recognizing it in practice."  
"That's how I always play! I am completely awesome!"  
"Witness your friend Twilight. She is more given to getting trapped in a thought pattern than most, but still capable of leaping out to a higher level of thought to look at things from another angle."  
"I was promised awesome pranks."  
"Witness." Mr Tortoise rapped loudly on library's silver knocker and held up a sign, which read, in small print " 'Produces falsehood when preceded by its own quotation' Produces falsehood when proceeded by its own quotation*" to the lavender unicorn who answered the door.  
"Oh! its a logic problem! Those are so fun!"  
"Huh, what's so great about a sign?"  
"Well, lets see, the phrase "produces falsehood when proceeded by its own quotation" could be either true or false. If its preceded by any other statement, it's true, but if it's preceded by itself then it's false, but it's the statement itself telling me that its false, _and_ the statement is wrong, so it's true. But if the statement is true, then I have to believe it when it tells me that its false."  
Twilight took a deep breath, while Mr Tortoise asked Spike to find him a copy of "Gidran, Friesian, Barb: a Recital Told in Neigh" by Egbert B. Goldsaddler.  
"But if its false, then we can't believe it when it says its false, so we should treat it as true."  
"Okay, the prank is awesome, but can we fix her now please? This is beginning to feel a bit like pranking Fluttershy."  
"But if its true, it says it is false and if it's false it's wrong when it says it's false."  
"She's getting faster. If she took half as long each time, she'd do an infinite number of iterations before you could catch up with me."

*Those peering very closely, would see that the the letters of the first iteration were made of many tinier letters, spelling, over and over "This statement is false", these words were in turn made of still tinier letters, spelling over and over, "this statement is true", and so on and so forth, all the way down to the Planck length. The second iteration was the same, but the order of "true" and "false" were reversed.

**Author's Note:**

> NEXT: Tortoise and Rainbow Dash demonstrate Zeno's arrow paradox.


End file.
